$\Delta$-filtrations and projective resolutions for the Auslander-Dlab-Ringel algebra

Abstract

The ADR algebra $R_A$ of an Artin algebra $A$ is a right ultra strongly quasihereditary algebra (RUSQ algebra). In this paper we study the $\Delta$-filtrations of modules over RUSQ algebras and determine the projective covers of a certain class of $R_A$-modules. As an application, we give a counterexample to a claim by Auslander-Platzeck-Todorov, concerning projective resolutions over the ADR algebra.

20 pages. Some small changes were done and typos were corrected. Accepted for publication in Algebras and Representation Theory

Cited by in corpus (5)

• The Ringel dual of the Auslander-Dlab-Ringel algebra
• Strongly quasi-hereditary algebras and rejective subcategories
• Ringel duality for certain strongly quasi-hereditary algebras
• Stratifying systems and Jordan-Hölder extriangulated categories
• On an upper bound for the global dimension of Auslander--Dlab--Ringel algebras